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Early modern domes built in the 18th century benefited from the newly developed mathematics of calculus and the study of statics. There were numerous studies on the catenary curve as the most stable form for arches and vaults and the ideal shape for a dome was debated in the late 18th century. Calculus allowed Guarini's experimental designs with intersections of spheres, barrel vaults, and oval domes to be proven and they would become the foundation of Rococo spatial arrangements.
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